Copy operations in shuffle and sort phase of MapReduce
Suppose you have 3 mappers and 1 reducer. Each mapper task outputs 1 file (sorted by key) that is written to the local filesystem of where the map function ran from. So, we will have 3 such output files spread around the cluster.
Since reducers do not take advantage of data locality optimisation, and since we have only 1 reducer - it will need to copy the 3 different output files that each mapper task produced across the network.
Hence, there are m x n = 3 x 1 = 3 copy operations involved in this scenario.